Loop animation of an imported image sequence in the video sequence editor
You just need to update the "final frame" of the rendering range, to make it fit your whole sequence: you can set it in the timeline header, or in the main "render"properties panel.

If you're using N chained copies of your sequence of X frames, just put "N*X" into that field and press enter: blender will calculate the final number and render that amount of frames...

Eg, if N=3 and X=240:





the result will be 720 frames, enough to contain your looped sequence in the final rendering.